Speak to your bank first. Go there well documented (payment slips, bank statements, bring a budget - how much are you spending today on rent, food, car, insurance, interest etc).
They can tell you how much you can borrow, based on the amount of your savings, income, etc. Usually this amount is a multiple of your annual household income. The lower the multiple and the higher the deposit you can make, the better the interest rate. Ask them to make you a written mortgage offer.
Go house hunting armed with that document. It gives you a big advantage over other buyers if the seller has to make a sale quickly. You will be taken more seriously and have a bigger chance of getting a lower price because the seller doesn't have to wait until you sort out financing. Your advantage is that you don't seem to be part of a chain - e.g. you don't need to sell your old house first before you can buy and you can therefore move quickly, make sure the seller understands that.